The ex-nova RR Pic presents a periodic hump in its light curve which is considered to refer to its orbital period. By analyzing all available epochs of these hump maxima in the literature and then combining them with those from new light curves obtained in 2013 and 2014, we establish an unique cycle count scheme valid during the past 50 years and derive an ephemeris with the orbital period 0.145025959(15) days. The O—C diagram of this linear ephemeris reveals systematic deviations that could have different causes. One of them could be a light-travel-time effect caused by the presence of a hypothetical third body near the star/brown dwarf mass limit, with an orbital period of the order of 70 years. We also examine the difficulty of the problematic of detecting substellar or planetary companions of close red-dwarf white-dwarf binaries (including cataclysmic variables) and discuss other possible mechanisms responsible for the observed deviations in O—C. For RR Pic, we propose strategies to solve this question by new observations.